Consider an Overlapping generations economy in which N, young individuals are born each period. Individuals are endowed with y = 15 units of the consumption good when young and nothing when old. The utility function of one typical agent is a typical time-separable CRRA: u(c], (2) = 4 , + AY.. Ac (0, 1] is the time discount factor and a > 0 is the inverse of the elasticity of intertemporal substitution. Population of the future generations are determined by Nitz = n.N, for all t 2 1, No = 100. 1. What is the equation for the feasible set of this economy? 2. Portray the feasible set on a graph. 3. Let's solve the Planner's Problem. (i) State the Planner's problem as a constrained maximization problem. (ii) Write down the Lagrangean for this problem. (iii) What are the FOCs? (iv) Assuming a stationary equilibrium, find the optimal allocations as a function of A, a and n only. 4. How does consumption when young respond to changes in 8? What about ? And n? 5. Now, 8 = 0.5 and o = 2 and n = 2. Substitute and find c] and cz